In this study, the relationship between chemical ordering, atomic pressures, and thermal stability in truncated octahedron nanoalloys of CuNPd(96-N)Ir44 compositions was investigated theoretically. The optimum chemical ordering was determined by scanning the potential energy surface using the Basin-Hopping algorithm. The results revealed that, for all compositions, iridium atoms (44 atoms) preferred to occupy the inner core of the nanoalloy, while palladium and copper atoms favored the outer surface. After optimizing the chemical ordering, the local pressures experienced by each atom were calculated. It was found that the core Ir atoms experienced positive local pressures, while the surface atoms (Cu and Pd) experienced negative pressures, with Cu atoms showing slightly lower pressures than Pd, indicating their relative instability on the surface. Additionally, thermal stability was analyzed through caloric curves, showing that Pd-rich compositions, such as Cu24Pd72Ir44, had a higher melting temperature (1246K) compared to Cu72Pd24Ir44 (1170K).